Answer:
0.25
Step-by-step explanation:
outcomes painted in blue: {3, 4, 5, 6}
number of even outcomes painted in blue: 2
number of total outcomes: 8
Therefore, the probability that the roll will show an even number and a face that is painted blue is: 2/8 = 0.25
Answer:
Equation of line b in standard form is: ![\mathbf{2x+y=-11}](https://tex.z-dn.net/?f=%5Cmathbf%7B2x%2By%3D-11%7D)
Option A is correct.
Step-by-step explanation:
We need to find equation of line b that passes through the point ( (6,4) and has a slope of -2.
First we need to find y-intercept of line using formula:
where m is slope and b is y-intercept.
Using m=-2 , x=6 and y=4 the y-intercept will be:
![y=mx+b\\4=-2(6)+b\\4=12+b\\b=4-12\\b=-11](https://tex.z-dn.net/?f=y%3Dmx%2Bb%5C%5C4%3D-2%286%29%2Bb%5C%5C4%3D12%2Bb%5C%5Cb%3D4-12%5C%5Cb%3D-11)
Now finding the equation of line having slope m=-2 and y-intercept b=-11
![y=mx+b\\y=-2x-11](https://tex.z-dn.net/?f=y%3Dmx%2Bb%5C%5Cy%3D-2x-11)
Writing the equation in standard form
![y=-2x-11\\2x+y=-11](https://tex.z-dn.net/?f=y%3D-2x-11%5C%5C2x%2By%3D-11)
So, equation of line b in standard form is: ![\mathbf{2x+y=-11}](https://tex.z-dn.net/?f=%5Cmathbf%7B2x%2By%3D-11%7D)
Option A is correct.
Answer:
Options (1), (2), (3) and (7)
Step-by-step explanation:
Given expression is
.
Now we will solve this expression with the help of law of exponents.
![\frac{\sqrt[3]{8^{\frac{1}{3}}\times 3} }{3\times2^{\frac{1}{9}}}=\frac{\sqrt[3]{(2^3)^{\frac{1}{3}}\times 3} }{3\times2^{\frac{1}{9}}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%5B3%5D%7B8%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%5Ctimes%203%7D%20%7D%7B3%5Ctimes2%5E%7B%5Cfrac%7B1%7D%7B9%7D%7D%7D%3D%5Cfrac%7B%5Csqrt%5B3%5D%7B%282%5E3%29%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%5Ctimes%203%7D%20%7D%7B3%5Ctimes2%5E%7B%5Cfrac%7B1%7D%7B9%7D%7D%7D)
![=\frac{\sqrt[3]{2\times 3} }{3\times2^{\frac{1}{9}}}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B%5Csqrt%5B3%5D%7B2%5Ctimes%203%7D%20%7D%7B3%5Ctimes2%5E%7B%5Cfrac%7B1%7D%7B9%7D%7D%7D)
![=\frac{2^{\frac{1}{3}}\times 3^{\frac{1}{3}}}{3\times 2^{\frac{1}{9}}}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B2%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%5Ctimes%203%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%7D%7B3%5Ctimes%202%5E%7B%5Cfrac%7B1%7D%7B9%7D%7D%7D)
![=2^{\frac{1}{3}}\times 3^{\frac{1}{3}}\times 2^{-\frac{1}{9}}\times 3^{-1}](https://tex.z-dn.net/?f=%3D2%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%5Ctimes%203%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%5Ctimes%202%5E%7B-%5Cfrac%7B1%7D%7B9%7D%7D%5Ctimes%203%5E%7B-1%7D)
![=2^{\frac{1}{3}-\frac{1}{9}}\times 3^{\frac{1}{3}-1}](https://tex.z-dn.net/?f=%3D2%5E%7B%5Cfrac%7B1%7D%7B3%7D-%5Cfrac%7B1%7D%7B9%7D%7D%5Ctimes%203%5E%7B%5Cfrac%7B1%7D%7B3%7D-1%7D)
![=2^{\frac{3-1}{9}}\times 3^{\frac{1-3}{3}}](https://tex.z-dn.net/?f=%3D2%5E%7B%5Cfrac%7B3-1%7D%7B9%7D%7D%5Ctimes%203%5E%7B%5Cfrac%7B1-3%7D%7B3%7D%7D)
[Option 2]
[Option 1]
![2^{\frac{2}{9}}\times 3^{-\frac{2}{3} }=(\sqrt[9]{2})^2\times (\sqrt[3]{\frac{1}{3} } )^2](https://tex.z-dn.net/?f=2%5E%7B%5Cfrac%7B2%7D%7B9%7D%7D%5Ctimes%203%5E%7B-%5Cfrac%7B2%7D%7B3%7D%20%7D%3D%28%5Csqrt%5B9%5D%7B2%7D%29%5E2%5Ctimes%20%28%5Csqrt%5B3%5D%7B%5Cfrac%7B1%7D%7B3%7D%20%7D%20%29%5E2)
![=(2^2)^{\frac{1}{9}}\times (3^2)^{-\frac{1}{3} }](https://tex.z-dn.net/?f=%3D%282%5E2%29%5E%7B%5Cfrac%7B1%7D%7B9%7D%7D%5Ctimes%20%283%5E2%29%5E%7B-%5Cfrac%7B1%7D%7B3%7D%20%7D)
[Option 3]
![2^{\frac{2}{9}}\times 3^{-\frac{2}{3} }=(2^2)^{\frac{1}{9}}\times (3^{-2})^{\frac{1}{3} }](https://tex.z-dn.net/?f=2%5E%7B%5Cfrac%7B2%7D%7B9%7D%7D%5Ctimes%203%5E%7B-%5Cfrac%7B2%7D%7B3%7D%20%7D%3D%282%5E2%29%5E%7B%5Cfrac%7B1%7D%7B9%7D%7D%5Ctimes%20%283%5E%7B-2%7D%29%5E%7B%5Cfrac%7B1%7D%7B3%7D%20%7D)
[Option 7]
Therefore, Options (1), (2), (3) and (7) are the correct options.
Answer:
Ans = 1980
Step-by-step explanation:
(10 x 100 ) + 980 = (1000) + 980
therefore
1980 is the answer
Answer:
The area of the regular octagon is ![293.72\ units^{2}](https://tex.z-dn.net/?f=293.72%5C%20units%5E%7B2%7D)
Step-by-step explanation:
we know that
The area of the regular polygon is equal to
![A=\frac{1}{2}Pa](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B1%7D%7B2%7DPa)
where
P is the perimeter of the regular polygon
a is the apothem
<em>Find the perimeter P</em>
![P=8(7)=56\ units](https://tex.z-dn.net/?f=P%3D8%287%29%3D56%5C%20units)
Find the area
![A=\frac{1}{2}(56)(10.49)=293.72\ units^{2}](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B1%7D%7B2%7D%2856%29%2810.49%29%3D293.72%5C%20units%5E%7B2%7D)